Fluctuation effects in metapopulation models: percolation and pandemic threshold

Metapopulation models provide the theoretical framework for describing disease spread between different populations connected by a network. In particular, these models are at the basis of most simulations of pandemic spread. They are usually studied at the mean-field level by neglecting fluctuations. Here we include fluctuations in the models by adopting fully stochastic descriptions of the corresponding processes. This level of description allows to address analytically, in the SIS and SIR cases, problems such as the existence and the calculation of an effective threshold for the spread of a disease at a global level. We show that the possibility of the spread at the global level is described in terms of (bond) percolation on the network. This mapping enables us to give an estimate (lower bound) for the pandemic threshold in the SIR case for all values of the model parameters and for all possible networks.Comment: 14 pages, 13 figures, final versio

Fractional diffusion emulates a human mobility network during a simulated disease outbreak

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.Comment: 26 pages, 4 figure

Recoverable prevalence in growing scale-free networks and the effective immunization

We study the persistent recoverable prevalence and the extinction of computer viruses via e-mails on a growing scale-free network with new users, which structure is estimated form real data. The typical phenomenon is simulated in a realistic model with the probabilistic execution and detection of viruses. Moreover, the conditions of extinction by random and targeted immunizations for hubs are derived through bifurcation analysis for simpler models by using a mean-field approximation without the connectivity correlations. We can qualitatively understand the mechanisms of the spread in linearly growing scale-free networks.Comment: 9 pages, 9 figures, 1 table. Update version after helpful referee comment

Epidemic modelling by ripple-spreading network and genetic algorithm

Mathematical analysis and modelling is central to infectious disease epidemiology. This paper, inspired by the natural ripple-spreading phenomenon, proposes a novel ripple-spreading network model for the study of infectious disease transmission. The new epidemic model naturally has good potential for capturing many spatial and temporal features observed in the outbreak of plagues. In particular, using a stochastic ripple-spreading process simulates the effect of random contacts and movements of individuals on the probability of infection well, which is usually a challenging issue in epidemic modeling. Some ripple-spreading related parameters such as threshold and amplifying factor of nodes are ideal to describe the importance of individuals’ physical fitness and immunity. The new model is rich in parameters to incorporate many real factors such as public health service and policies, and it is highly flexible to modifications. A genetic algorithm is used to tune the parameters of the model by referring to historic data of an epidemic. The well-tuned model can then be used for analyzing and forecasting purposes. The effectiveness of the proposed method is illustrated by simulation results

Dissemination of Health Information within Social Networks

In this paper, we investigate, how information about a common food born health hazard, known as Campylobacter, spreads once it was delivered to a random sample of individuals in France. The central question addressed here is how individual characteristics and the various aspects of social network influence the spread of information. A key claim of our paper is that information diffusion processes occur in a patterned network of social ties of heterogeneous actors. Our percolation models show that the characteristics of the recipients of the information matter as much if not more than the characteristics of the sender of the information in deciding whether the information will be transmitted through a particular tie. We also found that at least for this particular advisory, it is not the perceived need of the recipients for the information that matters but their general interest in the topic

Analytic Comparison of Some Epidemic Models with Vaccination

AbstractIn this paper, we discuss the elementary properties of some simple SI, SR, SIR and SEIR epidemic models whose parameterizing functions (such as per-capita death rate, disease transmission, removal rate etc.) might be eventually time-varying but nonnecessarily time-integrable. Vaccination rules based of feedback, measuring the numbers of some of the partial populations defining the disease progress, are also discussed

A Minimal Model for Multiple Epidemics and Immunity Spreading

Pathogens and parasites are ubiquitous in the living world, being limited only by availability of suitable hosts. The ability to transmit a particular disease depends on competing infections as well as on the status of host immunity. Multiple diseases compete for the same resource and their fate is coupled to each other. Such couplings have many facets, for example cross-immunization between related influenza strains, mutual inhibition by killing the host, or possible even a mutual catalytic effect if host immunity is impaired. We here introduce a minimal model for an unlimited number of unrelated pathogens whose interaction is simplified to simple mutual exclusion. The model incorporates an ongoing development of host immunity to past diseases, while leaving the system open for emergence of new diseases. The model exhibits a rich dynamical behavior with interacting infection waves, leaving broad trails of immunization in the host population. This obtained immunization pattern depends only on the system size and on the mutation rate that initiates new diseases

Modelling the interplay between human behaviour and the spread of infectious diseases: From toy models to quantitative approaches

Prevenir la propagació de malalties infeccioses és un dels reptes més grans de la humanitat. Moltes malalties es transmeten per contacte, per la qual cosa la xarxa d'interaccions humanes actua com a substrat per a la propagació. Per aquest motiu, els models epidèmics sempre inclouen, ja sigui implícita o explícitament, una descripció de com els éssers humans interactuen entre ells. Malgrat això, actualment no es disposa d’una teoria general de la interacció entre el comportament humà i la propagació d'agents. L’objectiu d’aquesta tesi és contribuir a la descripció matemàtica del comportament humà en el context de les malalties infeccioses, treballant tant amb models quantitatius com qualitatius. En el primer capítol es desenvolupen dos models qualitatius per entendre com l’adopció de mesures profilàctiques de manera dinàmica basada en el risc pot causar cicles epidèmics. En el segon capítol, considerem aspectes estàtics específics del comportament humà -homofília i patrons de contacte heterogenis- i n'analitzem les implicacions en el control d'epidèmies. En contrast amb el què es creia anteriorment, demostrem que l'homofília en l'adopció d’eines profilàctiques no sempre resulta perjudicial. A més a més, qüestionem el paradigma actual de les estratègies d'immunització basades en el risc. L'últim capítol d'aquesta tesi se centra en enfocs quantitatius per modelitzar la propagació del SARS-CoV-2, en particular la primera onada i la propagació de la variant Delta. A més dels avenços metodològics, mostrem com l’adaptació voluntària del comportament va determinar el curs de l’epidèmia més enllà de les intervencions no farmacèutiques. En conjunt, aquesta tesi revela una nova fenomenologia, afegeix proves empíriques addicionals i proporciona noves eines per analitzar com evolucionen el comportament humà i les epidèmies. La combinació d'enfocaments quantitatius i qualitatius també proporciona una via per analitzar i interpretar l’enorme quantitat de dades recopilades durant la pandèmia de SARS-CoV-2.Prevenir la propagación de enfermedades infecciosas es uno de los mayores retos de la humanidad. Muchas enfermedades se transmiten por contacto, por lo que la red de interacciones humanas actúa como sustrato para su propagación. Por esta razón, los modelos epidémicos siempre incluyen una descripción de cómo interactúan los seres humanos entre ellos. Sin embargo, actualmente no existe una teoría general de la interacción entre el comportamiento humano y la propagación de agentes. El objetivo de esta tesis es contribuir a la descripción matemática del comportamiento humano en el contexto de las enfermedades infecciosas, trabajando tanto con modelos cuantitativos como cualitativos. El primer capítulo desarrolla dos modelos cualitativos para esbozar cómo la profilaxis dinámica basada en el riesgo puede sostener ciclos epidémicos. En el segundo capítulo, consideramos aspectos estáticos específicos del comportamiento humano -homofilia y patrones de contacto heterogéneos- y analizamos sus implicaciones en el control de epidemias. En contraste con resultados anteriores, demostramos que la homofilia en la adopción de herramientas profilácticas no siempre es perjudicial. Además, cuestionamos el paradigma actual de las estrategias de inmunización basadas en el riesgo. El último capítulo de esta tesis se centra en enfoques cuantitativos para modelizar la propagación del SARS-CoV-2, en particular, la primera oleada y la propagación de la variante Delta. Además de los avances metodológicos, mostramos cómo la adaptación voluntaria del comportamiento fue capaz de determinar el curso de la epidemia más allá de las intervenciones no farmacéuticas. En conjunto, esta tesis desvela una nueva fenomenología, añade pruebas empíricas adicionales y proporciona nuevas herramientas para analizar cómo evolucionan el comportamiento humano y las epidemias. La combinación de enfoques cuantitativos y cualitativos proporciona una vía muy útil para analizar e interpretar la gran cantidad de datos recopilados durante la pandemia de SARS-CoV-2. Preventing the spread of infectious diseases is one of the greatest challenges of humanity's past, present, and foreseeable future. Many infectious diseases are transmitted upon contact, and hence the complex web of human interactions acts as a substrate for their propagation. For this reason, epidemic models always comprise, either explicitly or implicitly, a description of how humans interact. However, the quest for a general theory of the interplay between human behaviour and the spread of pathogens is far from complete. The aim of this thesis is to contribute to the mathematical description of human behaviour in the context of infectious diseases, working with both quantitative and qualitative models. The first chapter develops two qualitative toy models to outline how dynamical risk-based prophylaxis can sustain epidemic cycles. In the second chapter, we consider specific static aspects of human behaviour -- homophily and heterogeneous contact patterns -- and analyse their implications on epidemic control. In contrast to previous belief, we show that homophily in the adoption of many prophylactic tools is not always detrimental. Furthermore, we question the current paradigm of risk-based immunisation strategies and show that targeting hubs is only optimal for protection with high efficacy. The last chapter of this thesis focuses on quantitative approaches to model the spread of SARS-CoV-2, in particular, the first wave and the spread of the Delta variant. Besides the methodological advances, we add evidence of how voluntary behavioural adaptation shaped the course of the epidemic beyond non-pharmaceutical interventions. Overall, this thesis unveils new phenomenology, adds additional empirical evidence, and provides new tools to analyse how human behaviour and epidemics coevolve. The flexible blend of quantitative and qualitative approaches may also provide a pathway to analyse and interpret the vast amount of data currently collected during the SARS-CoV-2 pandemic